Thoughts on Teaching: 1

I spent about forty years teaching, first in economics departments and a business school then in law schools, and came up with a number of ideas about how it could be done better. Here are some of them.

An Application of Economics to Giving Exams

After answering the questions you know the answers to you still have time left so you answer the remaining questions in the hope that what you write will fool the professor grading the exam into thinking that you know at least part of the answer. Doing that costs you time writing and me time reading what you wrote. It lowers the quality of the information the exam produces, since there is a risk that I will either be fooled into giving you credit you do not deserve or fail to give another student partial credit he does deserve because I think he is bluffing.

My solution to this problem is an economic solution, but I like to claim that it was inspired by the story of Socrates and the Delphic Oracle.

Well, one day [Chaerephon] went to Delphi, and there he had the impudence to put this question -- do not jeer, gentlemen, at what I am going to say -- he asked, "Is anyone wiser than Socrates?" And the Pythian priestess answered, "No one." Well, I was fully aware that I knew absolutely nothing. So what could the god mean? for gods cannot tell lies. For some time I was frankly puzzled to get at his meaning; but at last I embarked on my quest. I went to a man with a high reputation for wisdom — I would rather not mention his name; he was one of the politicians — and after some talk together it began to dawn on me that, wise as everyone thought him and wise as he thought himself, he was not really wise at all. I tried to point this out to him, but then he turned nasty, and so did others who were listening; so I went away, but with this reflection that anyhow I was wiser than this man; for, though in all probability neither of us knows anything, he thought he did when he did not, whereas I neither knew anything nor imagined I did."

On my exams, knowing what you do not know was worth something — twenty percent. That was the fraction of the points for a question that you got for not doing it. If you suspect that the best bogus answer you can come up with will be worth less than twenty percent you are better off leaving the question blank and going home early, saving both of us time and me some of the hassle of trying to figure out which answers are or are not entirely bogus.

The Case for Short Exams

Another policy that I adopted many years ago was to try to make my exams short enough so that most students could finish before their time ran out. My original reason was my dissatisfaction with the practice of giving students who could persuade the relevant university officials that they had an invisible handicap, some sort of learning disability, extra time on exams. While some may have suffered from a real problem, I suspected that in many cases all that was special about their situation was having parents willing to pay a professional to produce the needed diagnosis. I did not like being a party to what I regarded as legalized cheating, had no way of preventing it, did have a way of making it ineffective. If everyone can finish the exam before time runs out, having an extra hour is no longer an advantage.

That was my original reason for trying to write sufficiently short exams. After I had been doing it for a while I concluded that it was a good idea on its own merits. In most contexts getting the right answer is more important than getting it quickly. An exam that most students find hard to complete rewards speed by more than I think it should be rewarded.

Another policy I followed was not to write the exam until after the last class. That way I did not have to worry, when answering questions in the final review class, that I might be giving away the answer to an exam question and so rewarding memory, not understanding.

The Use of Old Exams

University libraries often keep a file of old exams and make them available to students. One reason to do so is to help students study for  exams they are going to take. Another other may be to prevent students who have access to old exams from other sources, a friend who took the course the year before or a fraternity that keeps a file of old exams, from having an advantage over students who lack such access. A third possibility is that the practice is part of an elaborate charade: Let the students memorize the answers to last year’s exam, give more or less the same exam this year, and everyone can pretend that they have learned something when most of them haven’t.

My own practice was to cut out the middleman by webbing some of my old exams and linking to them on the class web page.

Should I web answers as well as questions? I never made up my mind either way, sometimes did, sometimes didn’t. One of the problems in teaching economics is that because it deals with features of the world that students are familiar with and uses ordinary language, often with specialized meanings, a student may go through a course thinking he understands everything but the fine points and end up having learned almost nothing. Providing answers makes it easier for a student to tell whether he actually understands the subject by how well his answer fits mine.

What I did not want the students to do and was concerned that many might attempt was to memorize the answers to the questions on past exams in the belief that some of them will appear on this year’s exam; memorizing an answer does not require you to understand it. That approach to studying goes along with the practice of going through a textbook using a highlighter to mark the five percent that you need to memorize because you expect to be tested on it, a practice that makes me wonder what the student thinks the rest of the book is there for.

My usual advice to the students was that, after studying for the midterm or final, they should take one of the webbed exams then compare their answers to mine to see if they are ready for the real exam. If the answers are not there a student can try to check his answers against the book or his lecture notes.

I tell my students how I want them to use the old exams but they may suspect, reasonably enough, that my objectives are not identical to theirs, that advice it is in my interest to give them may not be advice it is in their interest to follow. I therefor also warn the students that I try to avoid putting questions from the webbed exams on the current one, which may be more effective, providing they are paying attention, believe me, and remember.

At some level, my response to all such issues is that it is my  job to make it possible for students to learn, theirs to make it happen. If a student chooses to ignore my advice and devote his efforts to memorizing answers in order to get a good grade on the exam rather than learning ideas in order to understand what the course teaches, that is on him, not me. Along similar lines, I made no attempt to enforce compulsory attendance.

But I would still prefer to teach the course, so far as possible, in a way that makes it more likely that students end up understanding the ideas it covers.

Looking around the internet to see what other professors did with regard to old exams, I found a wide range of policies. Many universities provide copies of past exams, occasionally but not usually with answers, in some cases only making them available to their students; why they go to the trouble of keeping other people from seeing them I don’t know. There are web pages that link to exams from many universities, possibly contributed by students. One university, Texas Christian University, suspended 12 students for “allegedly using the Quizlet app to cheat on their exams.”¹ As best I could tell from the news story, the professor said that their offense was failing to tell him that they recognized questions on the exam as ones they had seen and studied on the app.

I can see two different arguments for trying to prevent students from studying past exams. One is paternalistic — that students will try to memorize answers to old exams and it won’t work, leaving them with neither a good grade nor understanding of the material of the course.  The other is that it will work, that the questions on this year’s exam will be sufficiently close to those on past exams so that memorizing the answers to old exams will be an adequate substitute for learning the course. If everything students can be tested on can be tested with a small enough number of questions so a student can memorize the answers to all of them that suggests that either there is not much content to the course or the professor is too lazy to write a different exam each year.

One commenter responded to my blog post on the subject with:

The best way to solve your exam problems, as well as many others, is to grant everyone a PhD, MD and JD at birth. Then classrooms would stop being polluted by students who didn't want to learn and those whose chief qualification is rich parents.

Just think how happy professors would be, teaching, like Socrates, only those who were desperate to improve themselves.

Which brings me to …

The Classes I Most Like Teaching

I have twice taught, as part of my university’s adult education program, an abbreviated version of my law school seminar on legal systems very different from ours — ten hours, divided into four or five lectures. Interested readers can find recordings of most of the more recent lectures and part of the earlier ones on the class web page. It was great fun.

There were two important differences between that class and most I have taught. The first was that nobody was there who was not interested in what I was teaching, since the class did not meet any requirement for getting a degree. The second was that I did not have to grade the students. It thus eliminated the two least attractive features of conventional teaching.

Each year I teach  ten or fifteen shorter classes of the same sort under rather different circumstances. The setting is the Pennsic War, an annual two week long historical recreation event held in a private campground in Pennsylvania. Attendance at the event is upwards of ten thousand people. My classes, most of them about an hour long, deal with medieval historical recreation — how to cook from a period recipe, make hardened leather armor, tell a period story in a way that creates the illusion of a medieval story teller entertaining a medieval audience. They are part of a Pennsic University that offers thousands of classes each year, all taught by volunteer teachers to volunteer students. Nobody is there to get a degree and nobody has to give any grades. Again more fun than my usual teaching.

Which suggests that perhaps there is something wrong with the alternative model employed for most teaching from kindergarten through college.

One comment on that blog post:

I taught ESL, which was very satisfying, since the students were always motivated; while they got no credit, they desperately needed English for jobs and schooling.

On the other hand, there's nothing worse than trying to teach Baby Physics or Baby Math to pre-law and pre-med students who take baby courses because they have to maintain their GPAs.

Unfortunately, someday you may be forced to hire one of them as a lawyer or be treated by one as a doctor.

Read then Listen or Listen then Read?

Most of the reading for the course I taught for many years on law and economics consisted of a book I wrote based on my lecture notes from previous iterations of the course. As in most courses, students were supposed to read each chapter before the first of the classes that discussed it.

I reach the point in the discussion at which I pose a puzzle to see if the students can work out the solution. It occurs to me that any student who has done the required reading already knows the answer, because it is in the book. I make a particularly telling point, summarize an argument with a punch line that I least believe to be witty; if a student reacts that is evidence that he has not read the assigned chapter, since it contains the same punch line. Large parts of the dramatic effect of the class only work for students who have not done the reading I assigned them.

I could use someone else's book — twenty some years earlier I did — but if there were another book on the subject I was happy with I would not have had to write mine. Alternatively, perhaps I could use my book and create an entirely new explanation of the ideas for class. I doubt I could do it and if I could I wouldn't; I would rather spend my time understanding and explaining some new set of ideas.

An easier alternative would be to reverse the order, assign each chapter to be read after the relevant class instead of before. That way the class introduces the ideas, the reading fills in details, reinforces what was discussed in class, gives the student a second chance to make sense of things he did not understand the first time through.

And I can deliver at least some of my punch lines to students who haven’t already seen them.

Another, perhaps better, possibility was suggested by a student; he said that he usually read a chapter after the first class in which the material was discussed but before the second. That way the material was fresh when he first heard it in class and he could use the second class to raise any questions that the reading had left him with.

One commenter on my blog raised the obvious question: Why, if the material I was covering was in the book, did I need to repeat it in my lecture? That question had occurred to me long before. After I wrote Price Theory, my first textbook, I tried the experiment of telling the students to read a chapter then come into class and tell me what they didn't understand or wanted to discuss; if nobody had anything to discuss we could go home. The students did not like it so I reverted to the more usual approach.

The puzzle of why they did not like it is related to my old puzzle of why the mass lecture, where there are too many students for significant interaction with the lecturer, did not vanish after the invention of the printing press. One possible answer is that some people learn better by listening than by reading. If so, the sensible arrangement would seem to be for some students to read the book and skip the lectures, some to attend the lectures and skip the book — a conclusion that I gather some students have worked out for themselves.

At Oxford and Cambridge, teaching is mostly done by a tutorial system, a weekly meeting with a tutor and one to three students. There are lectures but, according to some Oxford students I discussed the question with, most students don’t attend them.² That sounds a good deal closer to my ideal than the U.S. system.

1. The suspensions were eventually overturned but it is not clear whether other academic punishments were cancelled.

2. The discussion occurred after a talk I gave on education to the Karl Popper Society at Oxford. The talk and discussion are webbed.